How do you solve #8/9=(w-2)/6#?

1 Answer
Feb 13, 2017

Answer:

See the entire solution process below:

Explanation:

First, multiply each side by a common denominator for the fractions, in this case #color(red)(18)#, to eliminate the fractions while keeping the equation balanced:

#color(red)(18) xx 8/9 = color(red)(18) xx (w - 2)/6#

#cancel(color(red)(18)) 2 xx 8/color(red)(cancel(color(black)(9))) = cancel(color(red)(18)) 3 xx (w - 2)/color(red)(cancel(color(black)(6)))#

#16 = 3(w - 2)#

#16 = (3 xx w) - (3 xx 2)#

#16 = 3w - 6#

Next, add #color(red)(6)# to each side of the equation to isolate the #w# term while keeping the equation balanced:

#16 + color(red)(6) = 3w - 6 + color(red)(6)#

#22 = 3w - 0#

#22 = 3w#

Now, divide each side of the equation by #color(red)(3)# to solve for #w# while keeping the equation balanced:

#22/color(red)(3) = (3w)/color(red)(3)#

#22/3 = (color(red)(cancel(color(black)(3)))w)/cancel(color(red)(3))#

#22/3 = w#

#w = 22/3#